# NaHCO3 dissolved in water - how is pH calculated?

A buffer is a solution that has the ability to keep pH within a certain and narrow range: even if an excessof hydrogen ions (H+) is applied to the solution. In other words:buffers resist changes in pH whenreasonable amount of either H+ or OH- is added to the buffer solution.

There are many examples of buffers. Blood in humans is a well buffered system buffered by severalbuffers. Seawater is a buffer, and it is buffered around pH=8.4, mainly because of sodium bicarbonate.

The purpose of this particular webpage is to show how pH can be calculated in solution made bydissolving sodium bicarbonate (NaHCO3) in water.

## Example:

Consider a solution made of 0.1 M NaHCO3. The sodium bicarbonate will dissolve into Na+ andHCO3-. Furthermore, the HCO3- will partly split intofractions of CO2 and CO32-, respectively depending on pH. First ofall we should start by finding out what will happen to NaHCO3 when it dissolves in water.

This is easier than it might seem. We simply use the fact that the charge balance is always zero inan aqueous solution. From the pdf document about equilibrium, we know how to calculate the[CO2], [HCO3-] and [CO32-].In fact, it is not necessary to calculate the [CO2] but to help understand what is goingon, it' included in the following calculations that can also be seen in anexcel spreadsheet.

 Compound / ion Calculation [CO2]* TIC / (1 + Ka(CO2*) / [H+] + Ka(HCO3-).Ka(CO2*) / [H+]2) [HCO3-] TIC / (1 + [H+] / Ka(CO2*) + Ka(HCO3-) / [H+]) [CO32-] TIC / (1 + [H+]2 / (Ka(HCO3-).Ka(CO2*)) + [H+] / Ka(HCO3-))

In this case we are adding 0.1 M NaHCO3 we are adding 0.1 M Na+ and 0.1 M HCO3 that is distributedamong CO2*, HCO3- and CO32- depending on pH.This pH or [H+] is easily calculated (not considering ionic strength).

Step 1: A charge balance is established

It must be that [Na+] - [HCO3-] - 2.[CO32-] = 0.

If not, the charge balance is not zero andsomething is wrong. This equation can be fine-tuned to include [H+] and [OH-] so that theequations is:

[Na+] - [HCO3-] - 2.[CO32-] + [H+] - [OH-] = 0

We do not know either the [HCO3-] or the [CO32-] as the [H+] is unknown.

However, by trying out with the different [H+]s in the equation:

[Na+] - TIC / (1 + [H+] / Ka(CO2*) + Ka(HCO3-) / [H+]) - 2.TIC / (1 + [H+]2 / (Ka(HCO3-).Ka(CO2*)) + [H+] / Ka(HCO3-)) + [H+] - 10-14/[H+]= 0

it is seen that when [H+] is 10-8.31 the equation is fulfilled. This leads us to theconclusion that a 0.1 M NaHCO3 has a pH of 8.31. All calculations are shown in the excel spreadsheet. It is now up to the readerto figure out why the pH of 0.5 M NaHCO3 solution is also 8.31 and why only very, very dilutesolutions of NaHCO3 have a pH closer to 7.

This page is also available as a pdf-document that can be accessed by clicking here.

## Web resources  Question about acetate buffer This is the long and computational answer to Debra's question about what happens when 100 mmol of HCl ispoured into an 100 ml acetate buffer (0.2 M) 06.07.2019 Author: Jim ... Gases - the ideal gas law explained Chemical compounds in aqueous solutions are fairly easy to handle as their quantities can either be expressed in weight such as grams or kilos, moles perliter (molarity) or moles per kg (molality). Topic: pKa & Ka The basics ... Ions and compounds Atoms are made up of neutrons that are neutral and have no charge, protons with a positive charge andelectrons with a negative charge.An ion is an entity or a group of atoms with a positive or negative charge such as the positively charged hydrogen ion H+ and thenegatively charged nitrate ion NO3-. Negatively charged ions are also... pKa and Ka Background informationThe Ka value is a value used to describe the tendency of compounds or ions to dissociate. The Ka value is also called the dissociationconstant, the ionisation constant, and the acid constant.Topic: Equilibriums The pH scale The ...